An application of $\Gamma$-semigroups techniques to the Green's Theorem

TL;DR

This paper explores how $eta$-semigroup techniques can be applied to Green's Theorem, illustrating the transition from traditional semigroup theory to $eta$-semigroup frameworks.

Contribution

It demonstrates the application of $eta$-semigroup methods to Green's Theorem, bridging classical semigroup concepts with $eta$-semigroup structures.

Findings

Established a connection between Green's relations and $eta$-semigroups.

Provided a method to extend semigroup results to $eta$-semigroup contexts.

Showed the transition process from semigroups to $eta$-semigroups.

Abstract

The concept of a $\Gamma$-semigroup has been introduced by Mridul Kanti Sen in the Int. Symp., New Delhi, 1981. It is well known that the Green's relations play an essential role in studying the structure of semigroups. In the present paper we deal with an application of $\Gamma$-semigroups techniques to the Green's Theorem in an attempt to show the way we pass from semigroups to $\Gamma$-semigroups.